When you spill a drop of coffee, why is there always a dark ring at the outer edge on drying?

Why, when you spill a drop of coffee on your countertop, is there always a ring of dark stuff at the outer edge after it dries? Sidney Nagel and his colleagues at the University of Chicago wondered about it enough to find out that nobody actually knew the answer

This has implications for industries that rely on the uniform deposition of solids suspended in liquid media, paint, for example, and in protein crystallization, a problem familiar to molecular biologists trying to understand the structure of enzymes. Understanding the phenomenon also means that dispersed solids could be deposited in a controlled fashion, in creating tiny electronic circuits or providing a means of high-density information storage, for example.

“Why does all the material end up at the edge, when it starts out dispersed across the whole drop?” said Nagel, Professor in Physics and Associate Dean of the Physical Sciences Division. “This question actually effects many different types of processes, but I don’t think people had been aware of it as a scientific problem.”

Ring formation actually turns out to be a combination of factors: any surface roughness “pins” the edge of the drop, evaporation at the edges pulls more liquid, and suspended solids, out to the edge from the center. The flow piles the material up at the edges, where it eventually dries and forms a ring.

Co-authors on the Nature paper include graduate student Robert Deegan; Thomas Witten, Professor in Physics; and Todd Dupont, Professor in Computer Science and Mathematics, all from the Materials Research Science & Engineering Center at the University of Chicago, as well as former Chicago undergraduate Olgica Bakajin (now a graduate student at Princeton), and former Research Associate Greg Huber (now a postdoctoral fellow at the University of Arizona).

Nagel took notice of the coffee stains on his counter at home one morning and presented the problem to his MRSEC colleagues at an informal Friday lunch. “Everybody got excited about it, and everybody had explanations for it,” he said. “More and more people got involved in coming up with theories and doing experiments, people from math, computer science, chemistry, theoretical and experimental physics, and at all levels from undergraduate to senior faculty.”

In solving the coffee stain problem, Nagel and his colleagues undertook a series of simple experiments and calculations. “Almost every kind of experiment you can think of, you can do,” said Nagel. Does the type of solvent make a difference? No. Does the same thing happen with other similar materials, red wine, milk, tea, soup–yes. Different types of surfaces, metal, plastic, glass, still produced rings. In fact, even drying the drop upside down had no effect.

“Many off-the-cuff theories were proposed, and many tabletop experiments were done to check out these proposals,” said Witten, “and the more we played the more we realized that we didn’t understand it.”

Two undergraduates performed many of the preliminary experiments, examining chemical, thermal, polarity and gravitational effects, during a summer research program. Bakajin masked part of the drop and showed that the ring only formed on the unmasked portion, where it was free to evaporate. Covering the outer edge, while leaving the center free eliminated the ring entirely, leaving only a smudge in the center. Clearly, evaporation at the edge of the drop was important.

Experiments on a variety of surfaces showed that any surface roughness “pins' the edge of the drop so that it cannot shrink as the solvent evaporates. Because the perimeter remains fixed, the solvent, carrying the solute with it, streams to the edge to replace evaporated liquid.

During a review of the MRSEC, computer scientist Dupont heard about the ring-stain problem. He proposed the theory that an important feature might be that extra evaporation happens near the edge of the drop, because recondensation of evaporated material would happen less on the outside than in the middle.

“This suggestion was the first time we began to make quantitative progress on the problem,” said Witten, “because finally we had a basis to understand mathematically how the ring should grow with time and propose explicit things that could be tested. And in fact, Rob Deegan’s experiments showed that Todd’s basic idea was right.”

Deegan made a dispersion of particles that were big enough to see in a microscope but small enough that they wouldn’t fall to the bottom, so the movement of particles to the edge over time could be directly observed. The growth of the ring essentially followed the power law that Dupont had predicted. Looking at an evaporating drop under a microscope also confirmed the strong outward flow of material: all of the particles were streaming toward the edge, rather than moving around randomly.

“This whole project would not have been possible without a group effort,” said Witten. “No one of us individually would have taken this project seriously, but it grew collectively out of our common curiosity and interests, and this collective spirit is enhanced by a collaborative research grant to MRSEC by the National Science Foundation.”

MRSEC scientists have never lost their childlike fascination for the workings of the world around them. Among the physical phenomena they have studied are water drops, sand piles and mixed nuts. In each case, the studies have revealed fundamental physical laws underlying perplexing behavior, and provided insights that may have profound implications for industries such as mining, transportation, pharmaceuticals and construction.

Why do all the Brazil nuts always end up on the top of a jar of mixed nuts, for example? The answer: convection rolls generated when the jar is shaken trap the large nuts at the top. How many times do you have to tap a bag of ground coffee until it completely settles and doesn’t compact any more? The answer: you can tap it an infinite number of times and it will still find a bit more room to settle.

The convection rolls affect the mixing and transportation of, for example, mixtures of powdered grains of different sizes, something a pharmaceutical company wants to control in making pills. Compaction affects the preparation of building sites for construction, and roadbeds for paving.